## Fourier methods for mathematicians, scientists and engineers |

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Airy disc amplitude response function analogue angular frequency applied approximation atoms beam behaviour bell curve calculation cells co-domain coefficients complex components constant converge convolution theorem damped defined delta function density differential equations diffraction discrete effect electron energy equation of motion example extension oscillator finite follows force formula Fourier analysis Fourier expansion Fourier methods Fourier series Fourier theory Fourier transform function f(x graph harmonic equation impulse response input integrable function interval inversion theorem ions Laplace transform laser light limit linear low-pass filter mass Mathematics membrane multiples n-dimensional noise nucleus operator output periodic function phase photons polynomials position problem properties PSDF Radon transform range real-valued Riemann-Lebesgue lemma sampling function sequence shown in Fig shows signal simple sinusoidal smooth sound spatial spectral Suppose technique theory transfer function triangle wave two-dimensional values variables vector velocity wave wavelength zero